Prove that in a triangle ABC,:

sin(A)sin(B)sin(C) + cos(A)cos(B) = 1

implies:

A = B = 45° and C = 90°.

You can do a simple indirect proof here. Negate the implication, and try to prove that the assumption is no longer true. Hence, assume that (A is not B or A is not 45 degrees, or B is not 45 degrees) or C is not 90 degrees. Then you turn this into an indirect proof by cases. Standard proof procedure.

Posted by eleusive on 2004-02-28 23:37:55